This invention relates to wind energy conversion systems in general and, in particular, to a system which is sensitive to wind velocity for varying system configurations to provide a uniform output.
Windmills and other wind power conversion devices obtain power by converting, via blades, a column of moving air into an angular, mechanical motion.
An expression of the conversion factor is: the power contained in a cylinder of air of radius R, velocity V and density is given by EQU P=2.pi. R.sup.2 .rho. V.sup.3 ( 1)
neglecting rotational and drag losses, the work obtained per unit time P.sub.w is EQU P.sub.w= 2.pi. R.sup.2 .rho. V.sup.3 a(1 - a)2 (2)
Where R is the disc radius, a is the interference factor, and V and are as aforementioned.
The interference factor a is used to express the diminution of the velocity that occurs at the disk, where it is V(1 - a). Behind the windmill the diminution factor increases to an ultimate value of 2a. By obtaining the first derivative of P.sub.w with respect to a and solving it for zero, it can readily be seen from (2) that P.sub.w is maximum when a=.DELTA.. At this point P.sub.w for any values of R, or V is 59.2 percent of P, the power originally in the air, which represents the maximum conversion efficiency that can be obtained.
The axial thrust, representing the force tending to overturn a stationary windmill is given by EQU T=2 .pi.R.sup.2 .rho. V.sup.2 a(1 - a) (3)
This is maximum at a = 1/2and grows smaller with smaller values of a. Since the thrust is equivalent to the "drag" on an airplane, windmill designers try to minimize it by choosing smaller values of a and large radii. The result is a smaller percentage of power which can be taken from the air.
The percentage of power removed from the air is proportional to the power coefficient EQU P.sub.c = P/(.rho. R.sup.2 V.sup.3) (4)
It is a function of a, or of the geometric arrangement of the windmill and of the tip speed ratio 2 nR/V where n is the revolutions per second. P.sub.c has been determined empirically in windtunnel tests for various blade configurations.
Thus, for example, the American multiblade type used for pumping water on American farms utilizes about 30 percent of the kinetic energy of the wind, the Dutch four-arm type about 16 percent and the high speed propeller type (Stuart propeller) about 42%. The last type rotates at a tip speed 6 to 8 times the wind speed and is used widely in connection with electrical power generation. For two-blade propeller windmills having a diameter of D feet geared to electric generators of 70 percent efficiency the maximum kilowatt output in winds of velocity V fps is expressed approximately by the formula EQU kw = 0.376 .times. 10.sup..sup.-6 D.sup.2 V.sup.3 (5)
it has been shown that only 59.2 percent of the kinetic energy of the wind is theoretically recoverable; based on this consideration, a windmill of 70 percent aerodynamic efficiency and 90 percent gearing efficiency can be expected to have an overall conversion efficiency of 37 percent of the wind kinetic energy. In the existing art, the wind velocity, which enters into the power equation as cubed value and is considered to be beyond the designer's control is considered the governing factor in the usage and application of windpower. It is customary to consider wind velocities in terms of well defined groups and classify them as prevalent (frequent) winds and energy winds.
Prevalent winds blow five out of 7 days, while energy winds blow two out of 7 days. The mean prevalent velocity is 2 mph less than the average monthly velocity; the energy winds blow at velocities of about 2.3 times those of the prevalent winds and produce with the current state of the art three-fourths of the total energy in a given month. The wind of the highest energy has about 10 mph higher velocity than the most frequent wind. For each month the energy of all the varying winds adds up to double the amount that would be computed from the average hourly velocity of that month.
For the present state of the art, 8 mph yearly average is the minimum wind velocity practical for propeller type wheels. For the very light multiblades in present use which are mounted for bypass for winds above 15 mph, an operating range from 6 to 15 mph affords a monthly power output 14% greater than if the range were 8 to 15 mph.
The high wind regions of the United States, having 10 mph or more average yearly wind velocity are: a north-and-south strip 350 miles wide midway between the Atlantic and Pacific Oceans; the littoral of the Great Lakes; the Atlantic Seaboard; the Gulf Coast; and the Pacific Ocean near San Francisco and at the State of Washington. (See Tables 1 and 2).
Table 1 __________________________________________________________________________ Wind Velocities in the United States Avg Pre- Avg Pre- veloc- vailing Fast- veloc- vailing Fast- ity, direc- est ity, direc- est Station mph tion mile Station mph tion mile __________________________________________________________________________ Albany, N.Y. 9.0 S 71 Louisville, Ky. 8.7 S 68 Albuquerque, N.M. 8.8 SE 90 Memphis, Tenn. 9.9 S 57 Atlanta, Ga. 9.8 NW 70 Miami, Fla. 12.6 -- 132 Boise, Idaho 9.6 SE 61 Minneapolis, Minn. 11.2 SE 92 Boston, Mass. 11.8 SW 87 Mt. Washington, N.H. 36.9 W 150 Bismarck, N.Dak. 10.8 NW 72 New Orleans, La. 7.7 -- 98 Buffalo, N.Y. 14.6 SW 91 New York, N.Y. 14.6 NW 113 Burlington, Vt. 10.1 S 72 Oklahoma City, Okla. 14.6 SSE 87 Chattanooga, Tenn. 6.7 -- 82 Omaha, Neb. 9.5 SSE 109 Cheyenne, Wyo. 11.5 W 75 Pensacola, Fla. 10.1 NE 114 Chicago, Ill. 10.7 SSW 87 Philadelphia, Pa. 10.1 NW 83 Cincinnati, Ohio 7.5 SW 49 Pittsburgh, Pa. 10.4 WSW 73 Cleveland, Ohio 12.7 S 78 Portland, Maine 8.4 N 76 Denver, Colo. 7.5 S 65 Portland, Ore. 6.8 NW 57 Des Moines, Iowa 10.1 NW 76 Rochester, N.Y. 9.1 SW 73 Detroit, Mich. 10.6 NW 95 St. Louis, Mo. 11.0 S 91 Duluth, Minn. 12.4 NW 75 Salt Lake City, Utah 8.8 SE 71 El Paso, Tex. 9.3 N 70 San Diego, Calif. 6.4 WNW 53 Galveston, Tex. 10.8 -- 91 San Francisco, Calif. 10.5 WNW 62 Helena, Mont. 7.9 W 73 Savannah, Ga. 9.0 NNE 90 Kansas City, Mo. 10.0 SSW 72 Spokane, Wash. 6.7 SSW 64 Knoxville, Tenn. 6.7 NE 71 Washington, D.C. 7.1 NW 62 __________________________________________________________________________ U.S. Weather Bureau records of the average wind velocity, and fastest mile, at selected stations. The period of record ranges from 6 to 84 years, ending 1954. No correction for height of station above ground.
Table 2 __________________________________________________________________________ WINDMILLS Beaufort Scale of Wind Force (Compiled by U.S. Weather Bureau, 1955) Miles Terms used per in USWB hour Knots Wind effects observed on land forecasts __________________________________________________________________________ Less Less than 1 than 1 Calm; smoke rises vertically 1-3 1-3 Direction of wind shown by smoke drift; but not by wind vanes Light 4-7 4-6 Wind felt on face; leaves rustle; ordinary vane moved by wind 8-12 7-10 Leaves and small twigs in constant motion; wind extends light flag Gentle 13-18 11-16 Raises dust, loose paper; small branches are moved Moderate 19-24 12-21 Small trees in leaf begin to sway; crested wavelets form on inland waters Fresh 25-31 22-27 Large branches in motion; whistling heard in telegraph wires; umbrellas used with difficulty 32-38 28-33 Whole trees in motion; inconvenience felt walking Strong against wind 39-46 34-40 Breaks twigs off trees; generally impedes progress 47-54 41-47 Slight structural damage occurs; (chimney pots, Galees removed) 55-63 48-55 Seldom experienced inland; trees uprooted; considerable structural damage occurs Whole 64-72 56-63 Very rarely experienced; accompanied by widespread gale damage 73 or 64 or Very rarely experienced; accompanied by widespread more more damage Hurricane __________________________________________________________________________